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the illusion that mathematics is some sort of universal ground truth is dispelled once you understand what it means to prove something: it is not to construct a proof, but to convince other mathematicians that your proof makes sense. an inherently social activity
Mathematics is mechanically objective but fundamentally epistemological and hence embedded in subjective systems. I guess the difference is that if math is valid you can use it to build stuff and that stuff embodies the principles of the math. infinite but bounded valid maths
so you're saying that any math that can't be used to build stuff is invalid?
I think it becomes more like any other language in that case: it conveys information but doesn't necessarily correspond to anything in the world or have ontological significance for the world we actually live in. Modal logic is sort of like this: it's a sieve for intuitions.
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